The Keynan international has been in sensational form for the Scottish giants, prompting speculation he could be set for a move to the Premier League, with Manchester United and Arsenal interested.
And former-Celtic star Walker, who had two spells at Celtic Park, thinks Wanyama could be on his way for £10m.
"If they [Celtic] can attract a bid of around £9m or £10m for Wanyama, I'm absolutely convinced they'll sell him," said Walker.
The 21-year-old is suspended for Celtic's Champions League match against Spartak Moscow tonight, but the Bhoys can qualify for the knock-out round if they match Benfica's result against Barcelona.
Wanyama enjoyed a break-out display against Barcelona in the Champions League earlier this season at the Nou Camp. Celtic were 1-0 up against the Catalan club, only to slip to a last-minute 2-1 defeat, but Wanyama was superb that night, as he was in the return leg as Celtic won 2-1 at Celtic Park last month.
TalkSPORT reports Manchester United and Arsenal have both taken a look at Wanyama, who primarily operates as a defensive midfielder.
Manchester United have been linked with several central midfielders over the past few years, including replacements for Paul Scholes and Ryan Giggs, but Sir Alex Ferguson is yet to dip into the transfer market.
Over in north London, Arsene Wenger sold his defensive midfielder, Alex Song, to Barcelona in the summer, and the Gunners boss could be tempted to bid for Wanyama in the New Year.